Geometry response of glaciers to changes in spatial pattern of mass balance

The effect of the spatial pattern of mass balance on the steady-state geometry of a glacier is examined using a Vialov -Nye glacier-flow model based on non-linear internal deformation of the ice with no basal motion. Surface profiles are predicted using a range of spatial variations of mass balance that include uniform shifts that cause a change in the mean and spatial patterns with zero mean representing changes in balance gradient and curvature. The corresponding effect on geometry induced by the different mass-balance patterns are described in terms of the volume and measures of surface slope and convexity. The change in glacier volume, slope and convexity induced by uniform changes in mass balance with non-zero mean are more than one order of magnitude larger than corresponding changes caused by spatial patterns of similar amplitude, but with zero mean. These results show that the mean mass balance contains most of the mass-balance information relevant to the dynamic changes of a glacier. An important consequence is that the memory of a change in climate, which is controlled by the consequent volume change, should be insensitive to the spatial pattern other than how that affects the mean. The spatial pattern of mass balance does induce small changes in the shape of the steady-state profile, which indicates the spatial pattern could affect the short time-scale response characteristics.